Conservation of Energy and Spring Constant

[anniec123]

Homework Statement

In a physics lab experiment, a spring clamped to the table shoots a 22g ball horizontally. When the spring is compressed 22cm , the ball travels horizontally 5.2m and lands on the floor 1.4m below the point at which it left the spring. What is the spring constant?

Homework Equations

F=kΔx
kinetic energy final + potential energy final + spring energy final = kinetic energy initial + potential energy final + spring energy final

The Attempt at a Solution

Because the ball starts at rest, KE initial to 0. The initial spring energy = 1/2kx^2 (x=.22m). The initial PE = (.022 kg)(9.8)(1.4 m). I set all final energies = zero. So:
0+0+0=0+0.30184+1/2k(.22)^2
I solved for k and got 12.47, which was incorrect

Thanks in advance for your help!

 

[cepheid]

Welcome to PF anniec123!

It's not correct to set all final energies to 0, because the ball has non-zero kinetic energy at the end (at the instant it hits the floor).

Initially (after coming off the spring), all the ball's velocity is horizontal, and the horizontal component of its velocity never changes (because there are no horizontal forces acting, only gravity). If you could figure out what the ball's horizontal speed was, you could figure out how much kinetic energy was imparted to it by the spring, and from that, you can deduce the spring constant (since all of that kinetic energy must have initially been stored as elastic potential energy in the spring).

Ok, but how do you figure out the horizontal speed? Answer these questions:

1. How long does it take an object in free fall to fall by 1.4 m?
2. If the object moved *horizontally* by 5.2 m in the time that you calculated in (1), then what must its *horizontal* speed have been?